Bonferroni Correction

Definition

In Multiple Hypothesis Testing, the Bonferroni correction is a conservative method for probability thresholding to control the occurrence of false positives.

When deciding whether to accept or reject an individual null hypothesis, a probability threshold, α, is utilized to control the likelihood of false positives. In multiple hypothesis testing, an increased number of samples, n, in a given family increases the probability that false positives will arise within that family at the same probability threshold, α. Thus, the threshold, α, should be lowered to control the total number of false positives.

The Bonferroni correction controls the number of false positives arising in each family by using a probability threshold of α/nfor each observation within the family. By guaranteeing that the probability of a test being accepted within a family is the same as or less than the probability of any individual test being accepted, the Bonferroni correction is extremely conservative....